I agree with all of that. But that is not all you believe. You also believe your carnal nature has not been taken away. It is just those sins committed by it are forgiven.
My understanding is that our flesh refers to our body, not something that exists apart from it. There is a nature to a thing because there is that thing. "Flesh Nature" is not a Biblical term in fact. This never appears in the Bible. It simply speak of our flesh, sarx.
You had mentioned Strong's before, actually, I prefer to learn the meanings of Biblical words from the Bible itself. What I like to do is to look at every instance a particular word is used, and in each of it's forms. I'll often look at related words to get a better sense. For sure I start with lexicons, and my Greek class, but let's be honest, that was a long time ago.
I'll look at every instance a word is used, and look at the context, to see exactly how it's being used, and in relation to what. I'll generally find that I can sort the occurances, and sarx is an oft used word, so there are many, I can sort them into, "These show specific meaning by their context", and, "These do not show specific meaning by their context. An example would be,
Luke 24:39 KJV
Behold my hands and my feet, that it is I myself: handle me, and see; for a spirit hath not flesh and bones, as ye see me have.
This is plainly referring to Jesus' body.
John 8:15 KJV
Ye judge after the flesh; I judge no man.
This one, there isn't the same context to clarify, even if we expand our view,
John 8:14-16 KJV
14) Jesus answered and said unto them, Though I bear record of myself, yet my record is true: for I know whence I came, and whither I go; but ye cannot tell whence I come, and whither I go.
15) Ye judge after the flesh; I judge no man.
16) And yet if I judge, my judgment is true: for I am not alone, but I and the Father that sent me.
Jesus is speaking about coming from and going to heaven, that His judgment is true coming from His connection to His father. But there is no statement on what basis the Pharisees judge other than this to which we can compare it. For instance, were Jesus to have said, "you judge according to your own evil spirit", this would give us a context to say, "flesh" is used here in the same sense as "your own evil spirit". But there is no statement like that. We could go the other way, had He said, you judge as children of Adam, but there are not explanatory statements.
So I'd call the first to be unambiguous, and the second to be ambiguous, in that we need additional information to clarify exactly what it means, that is, unless it means just what the basic word itself means, "flesh", our physical being.
When I look at every occurance of "flesh" in this way, and divide between ambigous and unambiguous, I find that every passage that gives me a definitive context is the same, always about my physical being. "Flesh and bone", "my brothers according to the flesh," "flesh and blood", "eat the flesh of the Son of Man", "How can this man give us His flesh to eat?"
Some are particularly meaningful in this exploration. "The Word became flesh". Jesus did not become a sinful nature. "I will pour out my Spirit on all flesh".
So then I use this meaning to go back and understand those other passages,
John 3:6 KJV
That which is born of the flesh is flesh; and that which is born of the Spirit is spirit.
Romans 6:6-19 KJV
6) Knowing this, that our old man is crucified with him, that
the body of sin might be destroyed, that henceforth we should not serve sin.
7) For he that is dead is freed from sin.
8) Now if we be dead with Christ, we believe that we shall also live with him:
9) Knowing that Christ being raised from the dead dieth no more; death hath no more dominion over him.
10) For in that he died, he died unto sin once: but in that he liveth, he liveth unto God.
11) Likewise reckon ye also yourselves to be dead indeed unto sin, but alive unto God through Jesus Christ our Lord.
12)
Let not sin therefore reign in your mortal body, that ye should obey it in the lusts thereof.
13) Neither yield ye
your members as instruments of unrighteousness unto sin: but yield yourselves unto God, as those that are alive from the dead, and
your members as instruments of righteousness unto God.
14) For sin shall not have dominion over you: for ye are not under the law, but under grace.
15) What then? shall we sin, because we are not under the law, but under grace? God forbid.
16) Know ye not, that to whom ye yield yourselves servants to obey, his servants ye are to whom ye obey; whether of sin unto death, or of obedience unto righteousness?
17) But God be thanked, that ye were the servants of sin, but ye have obeyed from the heart that form of doctrine which was delivered you.
18) Being then made free from sin, ye became the servants of righteousness.
19)
I speak after the manner of men because of the infirmity of your flesh: for as ye have yielded your members servants to uncleanness and to iniquity unto iniquity; even so now yield
your members servants to righteousness unto holiness.
Your members, Body of sin, Your mortal body, this is our body parts and our bodies.
The infirmity of your flesh, is this the "weakness of the sinful nature", or,
Psalms 103:13-14 KJV
13) Like as a father pitieth his children, so the LORD pitieth them that fear him.
14) For he knoweth our frame; he remembereth that we are dust.
Acts 2:26 KJV
26) Therefore did my heart rejoice, and my tongue was glad; moreover also my flesh shall rest in hope:
Acts 2:31 KJV
31) He seeing this before spake of the resurrection of Christ, that his soul was not left in hell, neither his flesh did see corruption.
Romans 7:5 KJV
5) For
when we were in the flesh, the motions of sins, which were by the law, did work
in our members to bring forth fruit unto death.
Romans 7:18 KJV
18) For I know that in me (that is, in my flesh,) dwelleth no good thing: for to will is present with me; but how to perform that which is good I find not.
Romans 8:3 KJV
3) For what the law could not do, in that it was weak through the flesh,
God sending his own Son in the likeness of sinful flesh, and for sin, condemned sin in the flesh:
Can this really be saying God sent Jesus in the likeness of a "sin nature"?
I just don't see that.
Anyway, I wanted to give a more complete reply concerning Strong's definitions.
Much love!